The 'learn to box' comment was probably 'nough said, but here's a tip...

First of all work your footwork a lot more. Get your advancing footwork down so that you're not dragging your rear foot behind and get faster more explosive (off the ball of your rear foot) movement to propel yourself. The next thing is getting your distance and timing down. Sounds like youre not timing the coordination of the overall movement with the target youre advancing on. When youre in range and its time to fire the cross, drop your rear knee and pivot the ball of your foot simultaneously bringing your hip forward, and to do this while moving, you've got to get your rear leg up under you in the stance, not catching up still but caught up and digging the rear part of the ball of your foot into the canvas/mat like youre suddenly ready to start race, youve got to have sudden, explosive, positive traction under the ball of your foot to lever the energy off of.

When practicing against mits, heavy bag or sparring, think more of where you leg and ball of foot placement are in relation to firing the actual punch, then about your hand. Its your foot/leg/hip firing the punch thats key, and your hand is just the end of the projectile that pops when it reaches the target. Get that foot up under you, dig in so you can thrust your power (the foot can even make a loud pop on the floor when it hits its spot and rotates right). If youre reaching/dragging/lifting your foot you never will have a good cross. And establishing a good cross is a game changer when sparring so you need that to get anywhere.

Get used to punching and moving. Watch pro boxers do it. First thing I learnd to emulate this was to not drag my foot so much. Pick it up and make a quick step out of it.

If you are out of range, jab by steping in with lead leg, while pushing with the rear leg. Jab should land about the same time your lead leg hits the ground. This is all done in small steps.

From there, you should be in a situation where your momentum is still moving forward, as your rear foot picks up slightly and moves into your new position. From there, try stepping out (left for you) a little bit with your lead foot, while you throw a cross, with the rear foot firmly planted.

With regard to the 'perfect knockout' punch, I think this is a good part of the documentary, but when they move on to talking about deaaaddly ninja hammer fists, even the 'science' smells like bullshido.

The second video is kinda dumb too, though interesting. First of all, its hard to quantify the weight behind a punch thrown by a fighter. Much harder than just weighing 2 sumo wrestlers.
Secondly, the two things they are comparing is very different. I don't like seeing two very different things compared. One is pretty heavy but also very slow in velocity. Like comparing a paintball to a pistol bullet.
Last point has to do with the above, but with numbers. Once you bring the velocities closer together, the mass probably is much more important. A featherweight boxer with quick hands does not punch as hard as a heavyweight slugger.

I'd have much rather seen them compare say a punch of a lightweight boxer with a